Aleph_null Hypergravity in Three-Dimensions

Abstract

We construct hypergravity theory in three-dimensions with the gravitino \psi_{\mu m_1... m_n}{}^A with an arbitrary half-integral spin n+3/2, carrying also the index A for certain real representations of any gauge group G. The possible real representations are restricted by the condition that the matrix representation of all the generators are antisymmetric: (T^I)^{A B} = - (T^I)^{B A}. Since such a real representation can be arbitrarily large, this implies \aleph_0-hypergravity with infinitely many (\aleph_0) extended local hypersymmetries.